Shelly compared the number of oak trees to the number of maple trees as part of a study about hardwood trees in a woodlot. She counted 9 maple trees to every 5 oak trees. Later in the year there was a bug problem and many trees died. New trees were planted to make sure there was the same number of trees as before the bug problem. The new ratio of the number of map;e trees to the number of oal trees is 3:11. After planting new trees, there were 132 oak trees. How many more maple trees were in the woodlot before the bug problem than after the bug problem?

using cross multiplication,
11x = 396 divide both sides by 11 to get
x = 36
So now there are 36 maple trees.

Because there were new trees planted after the bugs to make the same number f trees before and after the bugs, we know there are 36 + 132 = 168 total trees. We use this total in the other proportion to solve.

Before the bugs, we know the ratio was 9 maple trees to 5 oak trees. However, this next proportion needs to find the number of maple trees using the total number of trees. So we add the trees in this ratio for a total number of trees to use in this ratio. 9 + 5 = 14. So the ratio of maple tree to the total number of trees is 9:14. This is used in the second proportion.